Diagonal of trapezium divide each other proportiona

AO/OC=BO/OD

4/4X-2=x+1/2x+4

4x²-2x+4x-2=8x+16

4x²+2x-2-8x-16=0

4x²-6x-18=0

2(2x²-3x-9)=0

2x²-3x-9=0

2x²-6x+3x-9=0

2x(x-3)+3(x-3)=0

(x-3)(2x+3)=0

x-3=0

x=3

or,2x+3=0

2x=-3

x= -3/2

x=-3/2 is not possible

So x=3